Horwell family: Difference between revisions

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__FORCETOC__
{{Technical data page}}
The horwell family of rank three temperaments tempers out the horwell comma, 65625/65536.
The '''horwell family''' of rank-3 temperaments tempers out the [[horwell comma]], 65625/65536 = {{monzo| -16 1 5 1 }}.


=Horwell=
== Horwell ==
Comma: 65625/65536
[[Subgroup]]: 2.3.5.7


7-limit minimax
[[Comma list]]: 65625/65536


[|1 0 0 0>, |16/7 6/7 -5/7 -1/7>,
{{Mapping|legend=1| 1 0 0 16 | 0 1 0 -1 | 0 0 1 -5 }}
|16/7 -1/7 2/7 -1/7>, |16/7 -1/7 -5/7 6/7>]


Eigenmonzos: 2, 7/6, 6/5
: mapping generators: ~2, ~3, ~5


9-limit minimax
[[Mapping to lattice]]: [{{val| 0 -1 1 -4 }}, {{val| 0 -1 0 -1 }}]


[|1 0 0 0>, |16/13 12/13 -5/13 -1/13>,
Lattice basis:
|32/13 -2/13 3/13 -2/13>, |32/13 -2/13 -10/13 11/13>]
: 5/4 length = 0.6213, 16/15 length = 1.3863
: Angle (5/4, 16/15) = 64.6379


Eigenmonzos: 2, 9/7, 7/5
[[Minimax tuning]]:  
* [[7-odd-limit]]
: {{monzo list| 1 0 0 0 | 16/7 6/7 -5/7 -1/7 | 16/7 -1/7 2/7 -1/7 | 16/7 -1/7 -5/7 6/7 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.7/3
* [[9-odd-limit]]
: {{monzo list| 1 0 0 0 | 16/13 12/13 -5/13 -1/13 | 32/13 -2/13 3/13 -2/13 | 32/13 -2/13 -10/13 11/13 }}
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.9/7


Lattice basis: 5/4 length=0.6213 16/15 length=1.3863
{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd }}


Angle(5/4, 16/15) = 64.6379
[[Badness]]: 0.173 × 10<sup>-3</sup>


Map to lattice: [&lt;0 -1 1 -4|, &lt;0 -1 0 -1|]
[[Projection pair]]: 7 65536/9375


Map: [&lt;1 0 0 16|, &lt;0 1 0 -1|, &lt;0 0 1 -5|]
== Zelda ==
[[Subgroup]]: 2.3.5.7.11


Generators: 2, 3, 5
[[Comma list]]: 385/384, 3388/3375


Edos: 9, 22, 25, 28, 31, 34, 40, 53, 56, 65, 75, 84, 87, 118, 140, 171, 824, 995
{{Mapping|legend=1| 1 0 0 16 -9 | 0 1 0 -1 2 | 0 0 1 -5 4 }}


Badness: 0.000173
{{Optimal ET sequence|legend=1| 22, 31, 53, 84, 87, 118, 258e, 376de, 547de }}


[[Projection_pair|Projection pair]]: 7 65536/9375
[[Badness]]: 0.642 × 10<sup>-3</sup>


=Horwellic=
== Horwellic ==
Commas: 3025/3024, 65625/65536
[[Subgroup]]: 2.3.5.7.11


Map: [&lt;1 0 0 16 10|, &lt;0 1 0 -1 1|, &lt;0 0 2 -10 -7|]
[[Comma list]]: 3025/3024, 65625/65536


EDOs: 31, 87, 118, 193, 224, 311, 342
{{Mapping|legend=1| 1 0 0 16 10 | 0 1 0 -1 1 | 0 0 2 -10 -7 }}


Badness: 0.000505
{{Optimal ET sequence|legend=1| 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee }}


=Zelda=
[[Badness]]: 0.505 × 10<sup>-3</sup>
Commas: 385/384, 3388/3375


Map: [&lt;1 0 0 16 -9|, &lt;0 1 0 -1 2|, &lt;0 0 1 -5 4|]
[[Category:Temperament families]]
 
[[Category:Pages with mostly numerical content]]
EDOs: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de, 665dee
[[Category:Horwell family| ]] <!-- main article -->
 
[[Category:Horwell| ]] <!-- key article -->
Badness: 0.000642
[[Category:Rank 3]]
 
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Planar temperament]]
[[Category:Horwell]]

Latest revision as of 00:38, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The horwell family of rank-3 temperaments tempers out the horwell comma, 65625/65536 = [-16 1 5 1⟩.

Horwell

Subgroup: 2.3.5.7

Comma list: 65625/65536

Mapping: [⟨1 0 0 16], ⟨0 1 0 -1], ⟨0 0 1 -5]]

mapping generators: ~2, ~3, ~5

Mapping to lattice: [⟨0 -1 1 -4], ⟨0 -1 0 -1]]

Lattice basis:

5/4 length = 0.6213, 16/15 length = 1.3863
Angle (5/4, 16/15) = 64.6379

Minimax tuning:

[[1 0 0 0⟩, [16/7 6/7 -5/7 -1/7⟩, [16/7 -1/7 2/7 -1/7⟩, [16/7 -1/7 -5/7 6/7⟩]
unchanged-interval (eigenmonzo) basis: 2.5/3.7/3
[[1 0 0 0⟩, [16/13 12/13 -5/13 -1/13⟩, [32/13 -2/13 3/13 -2/13⟩, [32/13 -2/13 -10/13 11/13⟩]
unchanged-interval (eigenmonzo) basis: 2.9/5.9/7

Optimal ET sequence: 22, 31, 53, 84, 87, 118, 140, 171, 1592c, 1763c, 1934c, 2074c, 2105c, 2245cd, 2416cd, 2587cd, 2758cd, 2929cd, 3100cd, 3271ccd, 3442ccd, 3613ccd, 5034bcccdd, 5205bcccdd

Badness: 0.173 × 10-3

Projection pair: 7 65536/9375

Zelda

Subgroup: 2.3.5.7.11

Comma list: 385/384, 3388/3375

Mapping: [⟨1 0 0 16 -9], ⟨0 1 0 -1 2], ⟨0 0 1 -5 4]]

Optimal ET sequence: 22, 31, 53, 84, 87, 118, 258e, 376de, 547de

Badness: 0.642 × 10-3

Horwellic

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 65625/65536

Mapping: [⟨1 0 0 16 10], ⟨0 1 0 -1 1], ⟨0 0 2 -10 -7]]

Optimal ET sequence: 31, 75e, 87, 118, 193, 224, 311, 342, 1592c, 1934ce, 2276cde, 2587cde, 2929cde, 3271ccde, 3613ccde, 5205bcccddee

Badness: 0.505 × 10-3

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